有界矩阵

In this project, we have tackled the robust fault detection and diagnosis problem for affine nonlinear sampled-data systems based on nonlinear H∞ filtering theory,and focused on the design of robust fault dtetction filter. The main contribution of this project is that we (1)present design methods of robust fault estimator for nonlinear discrete-time systems based on least square estimation and linear matrix inequality;(2)improve the bounded real lemma of systems with finite discrete jumps;(3)develop the robust fault detection filters for affine nonlinear sampled-data systems with parameter uncertainties based on the improved bounded real lemma.

本项目以提高故障的正确检测率为目的，以非线性H∞滤波理论为基础，对不确定仿射非线性采样系统的鲁棒故障检测与诊断问题进行了研究，重点研究了不确定仿射非线性采样系统的鲁棒故障检测滤波器设计问题，取得了一些新的成果，主要成果有：(1)基于最小二乘估计和线性矩阵不等式，给出了非线性离散系统的鲁棒故障估计器设计方法；(2)改进了有限跳跃点系统的有界实引理；（3）基于改进的有界实引理，给出了不确定仿射非线性采样系统的鲁棒故障检测滤波器的设计方法。

Without presuming the activation functions to be continuous, bounded and monotone nondecreasing, by utilizing linear matrix inequality and Cellina approximate selection theory in differential inclusion, a sufficient condition is provided to ensure existence of periodic solutions for that recurrent neural networks.

在并不要求激励函数连续、有界及单调非减的情况下，通过利用线性矩阵不等式和微分包含中的Cellina近似选择定理，得到了该神经网络模型存在周期解的充分条件。

The proposed method has the merit that the numerical characteristics of stochastic temperature field response can be obtained by analyzing the random temperature field just in one time.3. Perturbed numerical algorithm of nonprobabilistic convex set theoretical models on the temperature fieldThe uncertain parameters of physical parameters and initial boundary conditions of heat conduction are described by the convex model. The perturbation formulas of the upper and lower bounds of temperature field response with unknown-but-bounded parameters are given via the combination of matrix perturbation theory and the convex set theory model.4. Numerical analysis for transient temperature field with interval parametersConsidering the uncertainties of the transient heat transfer, the physical parameters and initial boundary conditions are regarded as interval variables.

该方法具有只进行一次随机温度场分析便可以获得其响应的数字特征的优点。3、温度场的非概率凸集合理论模型的摄动数值解法将结构导热的物理参数、温度场的初始和边界条件等不确定性参数以凸模型加以描述，基于矩阵摄动理论和处理不确定问题的凸集合理论模型的结合，导出有界不确定参数瞬态温度场响应所在集合的上、下界摄动计算公式。4、具有区间参数的瞬态温度场数值分析考虑结构瞬态热传导问题的不确定性，将结构各物理参数和温度的初、边值条件均视为区间变量。

Some results related to invertible matrices over bounded distributive lattice are generalized to matrices over incline.

将有界分配格上可逆矩阵的有关结果推广到坡上的矩阵。

Based on a delay-dependent bounded real lemma, the condition under which a decentralized robust H(subscript ∞) output feedback controller exists is derived and it is available to be attributed to a solution to the problem of nonlinear matrix inequality which can be expressed in terms of a homotopy function properly selected. Then, with the homotopic iteration method and the Schur complement lemma introduced, the solution can be converted into an iterative solution to the linear matrix inequality.

基于一个时滞依赖有界实引理，将系统鲁棒分散H动态输出反馈控制器的解归结为一个非线性矩阵不等式的求解问题；选取适当的同伦函数来表示该非线性矩阵不等式，采用同伦迭代算法及Schur补引理，将求解非线性矩阵不等式转化为线性矩阵不等式的迭代求解问题。

Chapter 3 is devoted to equistability and equiboundedness of matrix differential equations by making use of the symbol property of the matrix Liapunov function and its Dini derivate on specific set.

第三章研究了矩阵微分方程的渐近行为，给出了直接运用矩阵Liapunov函数在某特定集合上的符号与其广义Dini导数符号的性质研究矩阵微分方程的稳定性和有界性。

Following the definition of graph topology and network routing, a bounded neighbor discovery algorithm is proposed, and the upper bound on trips of any loop crossing one specified links is proved. A path generation algorithm based on the neighbor/path matrix is also presented and validated by some examples.

文中首先给出网络和路由的定义和表示；再提出基于有界扩散的邻接发现算法，并证明某一回路穿越特定链路次数的上界；然后提出基于邻接矩阵的路径生成算法，并给出实例分析以验证上述算法的正确性。

We first introduce the positive real spectrum function and bounded spectrum function then establish the parametrization of the power spectrum by the Levinson polynomials associated with the autocorrelation matrix of the output and bounded spectrum function.

首先引入正实谱函数的和有界谱函数的概念，利用正实函数和有界实函数理论，通过和过程自相关矩阵相关联的Levinson多项式和有界谱函数，建立了功率谱参数化的表达式。

Firsdy, using the linear matrix inequality method and the concept of finite-time boundness, some sufficient conditions of finite-time boundedness for the linear discrete systems with uncertain exogenous disturbance were derived.

针对一类不确定线性离散系统有限时间观测器最优设计问题，利用线性矩阵不等式方法以及有限时间有界的概念，给出了具有不确定外部扰动输入的线性离散系统有限时间有界的充分条件。

Considering the presence of large aerodynamic uncertainties in the process of flighting for launch vehicle and resilience vibration, liquid propellant rocking have a certain infulence on system, the design method of H〓 robust control systems with parameter uncertainties and unmodelled dynamics is researched.

首次对同时存在系统矩阵、控制输入矩阵的不确定和系统关联不确定变化以及有界能量干扰的关联大系统提出了一种简便的局部状态反馈分散H〓控制器的设计方法。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。